Characterizing postural balance on 2-dimensional compliant surfaces with directional virtual time-to-contact

Background: This study aimed to (1) investigate postural balance control on 2-Dimensional (2D) compliant surfaces using directional virtual time-to-contact (d-VTC), a novel method for VTC calculation; and (2) compare d-VTC with conventional balance measures in this context. Methods: A dual-axis robotic platform was used to simulate 2D surfaces/grounds with varying compliance levels. Twenty healthy young adults stood on the platform with either open or closed eyes. Balance was evaluated using d-VTC in multiple aspects, including temporal (VTC mean), spatial (boundary contact - BC), and control aspects (switching rate – SR). Additionally, conventional balance measures, namely center-of-pressure (COP) area and COP root-mean-square (RMS), were employed for further comparisons with d-VTC measures. Normality checks were performed using Shapiro-Wilk tests. Two-way repeated measures ANOVA tests were used to examine the effects of surface compliance and vision on postural balance, followed by post-hoc pairwise comparisons across conditions with Bonferroni correction. Results: The results showed that increasing surface compliance and/or absence of vision caused a significant decrease in VTC mean (all p-values <0.001; all η_p² > 0.816). Interaction effects between surface compliance and vision on 2D and ML VTC mean were also significant (all p-values <0.019; all η_p² > 0.355). The AP and ML BC values indicated a converging trend to 50%. No vision effect was observed (p = 0.458), but both surface compliance (p = 0.001; η_p² = 0.522) and interaction (p = 0.002; η_p² = 0.492) effects were significant. Decreases in SR were significant due to the compliance of the standing surface (p = 0.01; η_p² = 0.401) but not vision (p = 0.109). COP area increased due to both surface and vision conditions (all p-values <0.001; all η_p² > 0.872). AP and ML RMS were altered by vision (all p-values <0.001; all η_p² > 0.741), but not by surface condition (all p-values >0.06). No interaction effect was observed in the conventional measures (all p-values >0.07). Conclusion: Balance control is compromised by 2D compliant surfaces, which is exacerbated when vision is absent. Among all balance measures, VTC mean measures demonstrated particularly high sensitivity in identifying decreased balance capabilities, while BC and SR provided new insights into fall risks and balance control mechanisms. These insights may facilitate the development of rehabilitation training or assistive devices for fall prevention.